When two numbers are added, the positions of the addends are swapped, and the sum remains unchanged. a b=b a

To add three numbers, add the first two numbers first, or add the last two numbers first, and the sum remains unchanged. (a b) c=a (b c)

Appropriate use of the commutative law of addition and the associative law can reduce the difficulty of calculation.

If one addend increases (or decreases) by a number and the other addend remains unchanged, then their sum also increases (or decreases) by the same amount. a b=c ,a m b=c m, a-m b=c-m , (a m) (b-n)=c m-n,

If one addend increases (or decreases) by a number and another addend decreases (or increases) by the same amount, then their sum does not change. (a m) (b-m)=c

Subtracting two consecutive numbers from a number is equal to this number minus the sum of the two numbers. a-b-c=a-(b c)

Subtracting the difference of two numbers from a number is equal to subtracting the minuend from the difference and then adding the subtrahend to the number. a-(b-c)=a-b c

When removing parentheses, if there is a minus sign outside the parentheses, the sign inside the parentheses will change; if there is a plus sign outside the parentheses, the sign inside the parentheses will not change.

If the minuend increases (or decreases) by a number and the minuend does not change, then their difference also increases (or decreases) by the same amount. If a-b=c then (a±m)-b=c ±m

If the minuend and minuend remain unchanged and the subtrahend increases (or decreases) by a number, then their difference decreases (or increases) by the same amount.

If the minuand and subtrahend increase (or decrease) by the same amount at the same time, their difference remains unchanged.

Subtraction is the inverse operation of addition

Addend Addend = sum, and - addend = another addend.

Minuend - Minuend = Difference, Minuend - Difference = Minuend, Difference Minuend = Minuend

Using the above relations, you can perform calculations of addition and subtraction.

The simple operation of finding the sum of several identical addends is called multiplication.

Factor × factor = product a × b =c

Align the end, multiply from the ones digit, multiply the number in each digit of the factor by another factor; multiply by the number in which digit of the factor, the last digit of the resulting product will be aligned with that digit, and finally multiply the number of times The products of the multiplications add up.

Product ÷ one of the factors = the other factor; use the commutative law of multiplication to exchange the positions of the two factors and calculate again.

When two numbers are multiplied together, the positions of the two numbers are swapped, and the product remains unchanged. a×b=b×a

Note: The commutative law of multiplication applies to expressions that only contain multiplication operations.

To multiply three numbers, multiply the first two numbers first, or multiply the last two numbers first, and the product remains unchanged. (a×b)×c=a×(b×c)

law

application

One factor remains unchanged, the other factor multiplies (or divides) a number that is not 0, and their product also multiplies (or divides) this number. a ×b=c, a÷m×b=c÷m , a×m×b=c×m (m≠0)

When one factor multiplies (or divides) a number that is not 0, and another factor divides (or multiplies) that number, their product remains unchanged. a ×b=c, a×m×(b÷m)=c (m≠0)

If the product of two factors and one of the factors is known, the operation of finding the other factor is called division. Division is the inverse operation of multiplication.

When 0 is divided by any number that is not 0, the quotient is 0, that is, 0÷a=0 a≠0

It is necessary to distinguish between dividing and dividing by. For example: 9÷3 can be read as 9 divided by 3, or as 3 divided by 9.

Dividend ÷ divisor = quotient.....remainder. For example: 14÷5=2.....4

In integer division with a remainder, the remainder must be smaller than the divisor. The largest remainder is 1 less than the divisor.

Divisor = Quotient × Divisor Remainder; Divisor = (Divisor - Remainder) ÷ Quotient

"Divisor = quotient × divisor remainder" is often used to check division formulas with remainders.

Starting from the highest digit of the dividend, the number of the divisor depends on the first few digits of the dividend. If the first few digits are smaller than the divisor, then take one more digit and divide. Which digit is divided to, the quotient is written there. One of the top.

If the quotient of any digit of the dividend is less than 1, then write "0" in that digit.

The remainder of each division must be smaller than the divisor.

When the divisor is close to a whole ten or a hundred, the divisor is usually treated as a whole ten or a hundred to test the quotient.

Test the quotient by treating the dividend and divisor together as positive tens, whole hundreds, or tens and hundreds.

A number divided by two numbers is equal to the number divided by the product of the two numbers. a÷b÷c=a÷（b×c) b≠0，c≠0.

In division, the dividend and divisor are simultaneously (or divided by) the same number (except 0), and the quotient remains unchanged. (a×c)÷(b×c)=a÷b (c≠0); (a÷c)÷(b÷)=a÷b (c≠0)

In division with a remainder, if the dividend and the divisor are at the same time (or divided by) the same number (except 0), the quotient remains unchanged, but their remainders must be multiplied (or divided) by this number.

If the dividend is multiplied (or divided) by a number other than 0 and the divisor remains unchanged, then their quotient must also be multiplied (or divided) by the same number. a÷b=c ,( a×n)÷b=c×n ; (a÷n)÷b=c÷n (n≠0)

If the dividend remains unchanged and the divisor is multiplied (or divided) by a number other than 0, and the divisor remains unchanged, then their quotient will be divided (or multiplied) by the same number. a÷b=c, a÷（b×n)=c÷n; a÷（b÷n)=c×n (n≠0）

Division is the inverse operation of multiplication.

Factor × factor = product, factor = product ÷ factor, dividend ÷ divisor = quotient, dividend ÷ quotient = divisor, dividend = quotient × divisor.

Check using the commutative law of multiplication

Check with division

Check with multiplication

Check with division: Swap the divisor and quotient.

Calculation of division with remainder: dividend = divisor × quotient remainder.

Addition, subtraction, multiplication, and division are collectively called the four arithmetic operations.

In a calculation, two or more of the four operations of addition, subtraction, multiplication, and division are called four mixed operations.

Among the four mixed operations, addition and subtraction are called first-level operations, and multiplication and division are called second-level operations.

Only addition and subtraction or only multiplication and division: Calculate from left to right.

There are both multiplication and division, as well as addition and subtraction: multiplication and division first, then subtraction.

Only parentheses: first calculate what is inside the parentheses, then what is outside the parentheses.

There are parentheses and square brackets: first calculate what's inside the small brackets, then what's inside the square brackets, and finally what's outside the square brackets.